TY - JOUR
AU - Brazelton, Thomas
AU - McKean, Stephen
PY - 2023/02/20
Y2 - 2024/02/26
TI - Lifts, transfers, and degrees of univariate maps
JF - MATHEMATICA SCANDINAVICA
JA - Math. Scand.
VL - 129
IS - 1
SE - Articles
DO - 10.7146/math.scand.a-134457
UR - https://www.mscand.dk/article/view/134457
SP -
AB - <p>One can compute the local $\mathbb{A}^1$-degree at points with separable residue field by base changing, working rationally, and post-composing with the field trace. We show that for endomorphisms of the affine line, one can compute the local $\mathbb{A}^1$-degree at points with inseparable residue field by taking a suitable lift of the polynomial and transferring its local degree. We also discuss the general set-up and strategy in terms of the six functor formalism. As an application, we show that trace forms of number fields are local $\mathbb{A}^1$-degrees.</p>
ER -